Internal problem ID [10360]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag, NY.
2015.
Section: Chapter 1, First order differential equations. Section 1.3.1 Separable equations. Exercises page
26
Problem number: 4(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (2 u+1\right ) u^{\prime }-1-t=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve((2*u(t)+1)*diff(u(t),t)-(1+t)=0,u(t), singsol=all)
\begin{align*} u \left (t \right ) = -\frac {1}{2}-\frac {\sqrt {2 t^{2}+4 c_{1} +4 t +1}}{2} \\ u \left (t \right ) = -\frac {1}{2}+\frac {\sqrt {2 t^{2}+4 c_{1} +4 t +1}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.102 (sec). Leaf size: 55
DSolve[(2*u[t]+1)*u'[t]-(1+t)==0,u[t],t,IncludeSingularSolutions -> True]
\begin{align*} u(t)\to \frac {1}{2} \left (-1-\sqrt {2 t (t+2)+1+4 c_1}\right ) \\ u(t)\to \frac {1}{2} \left (-1+\sqrt {2 t (t+2)+1+4 c_1}\right ) \\ \end{align*}